Question

A venture investor, SoCAL is considering investing in a software venture opportunity. However, the rate of return to be realized next year is likely to vary with the economic climate that actually occurs as below. Calculate the coefficient of variation (CV) of the rates of return for the software venture.

   Economic        Probability of               Rate of

      Climate            Occurrence                  Return

      Recession              .25                         -15.0%

      Normal .50                          15.0%

      Rapid growth        .25                             30.0%

Answer 1

Expected return=Respective return*Respective probability

=(0.25*-15)+(0.5*15)+(0.25*30)

=11.25%

probability	Return	probability*(Return-Expected Return)^2
0.25	-15	0.25*(-15-11.25)^2=172.265625
0.5	15	0.5*(15-11.25)^2=7.03125
0.25	30	0.25*(30-11.25)^2=87.890625
		Total=267.1875%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)

=(267.1875)^(1/2)

=16.35%(Approx)

Coefficient of variation=Standard deviation/Expected return

=16.35/11.25

=1.453(Approx)